Spatially-selective reflector structures, reflector disks, and systems and methods for use thereof

ABSTRACT

The invention provides a spatially-selective reflective structure for the detection of submillimeter electromagnetic waves and systems and methods incorporating spatially-selective reflective structures. One aspect of the invention provides a spatially-selective reflective structure including a partially-conducting slab and a modulating reflector disk adjacent to the partially-conducting slab. The modulating reflector disk includes a plurality of modulations. Another aspect of the invention provides a submillimeter imaging device including submillimeter wave optics, a spatially-selective reflective structure located in the focal plane of the submillimeter wave optics, a submillimeter wave receiver positioned to capture waves reflected from the spatially-selective reflective structure, and a motor configured to rotate the spatially-selective reflective structure. The spatially-selective reflective structure includes a partially-conducting slab and a modulating reflector disk adjacent to the partially-conducting slab. The modulating reflector plate includes one or more modulations.

CROSS-REFERENCES TO RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 61/155,316, filed Feb. 25, 2009, and U.S. Provisional PatentApplication Ser. No. 61/301,433, filed Feb. 4, 2010. The contents ofthese patent applications are hereby incorporated by reference in theirentirety.

BACKGROUND

Terrorist attacks over the last decade have heightened securityrequirements at a host of locations and activities such as airports,sporting events, political gatherings, and the like. Security stationsat these locations must process large numbers of individuals in anefficient manner while providing effective screening for weapons andcontraband.

Screening for concealed weapons is a particularly challenging task. Manyindividuals have a variety of metallic items in or on their person (e.g.prostheses, jewelry, belt buckles, coins), thereby impairing theeffectiveness of conventional metal detectors. Moreover, weapons can befabricated from non-metallic materials that cannot be detected withconventional metal detectors. Backscatter X-ray devices exist fordetecting such concealed devices, but require that an individual standclose to a flat panel and raise health concerns due to ionizingradiation exposure.

Accordingly, it would be desirable to provide a device that providesimproved-resolution imaging of concealed objects without the need forionizing radiation.

SUMMARY OF THE INVENTION

The invention provides a spatially-selective reflective structure forthe detection of submillimeter electromagnetic waves and systems andmethods incorporating spatially-selective reflective structures.

One aspect of the invention provides a spatially-selective reflectivestructure including a partially-conducting slab and a modulatingreflector disk adjacent to the partially-conducting slab. The modulatingreflector disk includes one or more modulations.

This aspect of the invention can have several embodiments. The one ormore modulations can be a single modulation. The one or more modulationscan be a plurality of modulations. The plurality of modulations can bearranged in a spiral pattern. The plurality of modulations can bearranged randomly.

The plurality of modulations can be arranged such that a matrix having aplurality of rows, each with elements corresponding to a fraction ofeach pixel in a viewing window projected onto the disk that is backed bya modulation at a distinct rotational position of the disk, has linearlyindependent rows.

The plurality of modulations can be separated by a multiple of awavelength of interest. The multiple can be an odd multiple. Themultiple can be greater than five.

The modulations can have well-defined edges. The partially-conductingslab can be a semiconductor. The partially-conducting slab can be adielectric doped with conductive particles. The partially-conductingslab can include a non-conductive plate and a thin metal film applied tothe non-conductive plate.

The modulating reflector disk can include a highly-conductive metal. Thepartially-conducting slab and the modulating reflector disk can becoupled with one or more mechanical fasteners. The modulating reflectordisk can rotate independently of the partially-conducting slab.

The partially-conducting slab and the modulating reflector disk can beseparated by a gap. The gap can be adjustable. The modulations can bedepressions or bumps.

The modulations can have a cross-sectional dimension greater or equal toabout one wavelength of interest. The one or more modulations can have across-sectional dimension greater or equal to three wavelengths ofinterest. The one or more modulations can have a cross-sectionaldimension less than the wavelength of interest multiplied by an F-numberfor an optics system directing radiation at the spatially-selectivereflective structure.

The distance between the modulations of the modulating reflector diskand the partially-conducting slab can be defined by the formula

${d_{n} = {n\frac{\lambda}{2\sqrt{ɛ_{r}{\cos\left( \phi_{i} \right)}}}}},$n=1, 2, . . . , wherein ε_(r) is the relative permittivity of the mediabetween the partially-conducting slab and the modulations, λ is thewavelength of interest, and φ_(i) is the angle of radiation incidencegiven with respect to a normal of the spatially-selective reflectivestructure.

The distance between a non-modulated surface of the modulating reflectordisk and the partially-conducting slab can be defined by the formula

${d_{r} = \frac{\left( {{2n} - 1} \right)\lambda}{4\sqrt{ɛ_{r}}{\cos\left( \phi_{i} \right)}}},$n=1, 2, . . . wherein ε_(r) is the relative permittivity of the mediabetween the partially-conducting slab and the modulations, λ is thewavelength of interest, and φ_(i) is the angle of radiation incidencegiven with respect to a normal of the spatially-selective reflectivestructure.

Another aspect of the invention provides a submillimeter imaging deviceincluding submillimeter wave optics, a spatially-selective reflectivestructure located in the focal plane of the submillimeter wave optics, asubmillimeter wave receiver positioned to capture waves reflected fromthe spatially-selective reflective structure, and a motor configured torotate the spatially-selective reflective structure. Thespatially-selective reflective structure includes a partially-conductingslab and a modulating reflector disk adjacent to thepartially-conducting slab. The modulating reflector plate includes oneor more modulations.

This aspect of the invention can have several embodiments. The devicecan further include a submillimeter wave source. The spatially-selectivereflective structure can be positioned to selectively reflectsubmillimeter waves from an image formed on the spatially-selectivereflective structure by the submillimeter wave optics to thesubmillimeter wave receiver. The submillimeter wave optics can include afocusing mirror. The motor can rotate the spatially-selective reflectivestructure at about 1,800 revolutions per minute. The receiver cancapture images at a rate of about 30 frames per second.

The plurality of modulations can be arranged in a spiral pattern. Theplurality of modulations can be arranged in randomly. The plurality ofmodulations can be arranged such that a matrix having a plurality rows,each with elements corresponding to a fraction of each pixel in aviewing window projected onto the disk that is backed by a modulation ata distinct rotational position of the disk, has linearly independentrows. The submillimeter imaging device can include a shield defining aviewing window on the spatially-selective reflective structure

Another aspect of the invention provides a method of submillimeterimaging. The method includes providing submillimeter wave optics, aspatially-selective reflective structure located in the focal plane ofthe submillimeter wave optics, a submillimeter wave receiver positionedto capture waves reflected from the spatially-selective reflectivestructure, and a motor configured to rotate the spatially-selectivereflective structure; actuating the motor to rotate thespatially-selective reflective structure; capturing a plurality ofreflections from the plurality of modulations as the spatially-selectivereflective structure rotates; storing each of the plurality ofreflections as a pixel; and forming an image from the plurality of thepixels. The spatially-selective reflective structure includes apartially-conducting slab and a modulating reflector disk adjacent tothe partially-conducting slab. The modulating reflector plate includes aplurality of modulations.

This aspect of the invention can have several embodiments. The methodcan include storing the image, displaying the image, and/or performingan image recognition method on the image. The storing and forming stepscan be performed on a computer.

Another aspect of the invention provides a method of submillimeterimaging. The method includes: providing submillimeter wave optics, aspatially-selective reflective structure located in the focal plane ofthe submillimeter wave optics, a submillimeter wave receiver positionedto capture waves reflected from the spatially-selective reflectivestructure, and a motor configured to rotate the spatially-selectivereflective structure; actuating the motor to rotate thespatially-selective reflective structure; capturing a plurality ofreflections from the plurality of modulations as the spatially-selectivereflective structure rotates; solving a system of equations wherein amagnitude of one of the plurality of reflections is equal to a sum of aproduct of the reflection in each of a plurality of pixels and thefraction of pixel area backed by the plurality of modulations; andforming an image from the plurality of the pixels. Thespatially-selective reflective structure includes a partially-conductingslab and a modulating reflector disk adjacent to thepartially-conducting slab. The modulating reflector plate includes aplurality of modulations.

This aspect of the invention can have several embodiments. The number ofequations in the system of equations can be equal to the numberreflections captured. The plurality of modulations can be arranged suchthat a matrix having a plurality rows, each with elements correspondingto a fraction of each pixel in a viewing window projected onto the diskthat is backed by a modulation at a distinct rotational position of thedisk, has linearly independent rows. The solving and forming steps canbe performed on a computer.

Another aspect of the invention provides a reflector disk including ametal disk having one or more modulations, a dielectric coupled to themetal disk, and a metal film coupled to the dielectric.

Another aspect of the invention provides a method of fabricating areflector disk. The method includes applying a dielectric to a metaldisk having one or more modulations and applying a metal film to thedielectric.

This aspect of the invention can have a variety of embodiments. Themethod can include forming the one or more modulations. The method caninclude machining the dielectric to produce uniform surface prior toapplying the metal film.

Another aspect of the invention provides a profiling scanner including aproximal end, a distal end, a first submillimeter imaging device, and asecond submillimeter imaging device. The first submillimeter imagingdevice includes: a first spatially-selective reflective structure, afirst submillimeter wave receiver positioned to capture waves reflectedfrom the first spatially-selective reflective structure, and a firstmotor configured to rotate the first spatially-selective reflectivestructure. The first spatially-selective reflective structure includes afirst partially-conducting slab and a first modulating reflector diskadjacent to the first partially-conducting slab. The first modulatingreflector plate includes one or more modulations. The secondsubmillimeter imaging device includes: a second spatially-selectivereflective structure, a second submillimeter wave receiver positioned tocapture waves reflected from the second spatially-selective reflectivestructure, and a second motor configured to rotate the secondspatially-selective reflective structure. The second spatially-selectivereflective structure includes a second partially-conducting slab and asecond modulating reflector disk adjacent to the secondpartially-conducting slab. The second modulating reflector plateincludes one or more modulations.

This aspect of the invention can have a variety of the embodiments. Inone embodiment, the profiling scanner includes a moving walkwayconfigured to carry an individual from the proximal end to the distalend.

FIGURES

For a fuller understanding of the nature and desired objects of thepresent invention, reference is made to the following detaileddescription taken in conjunction with the accompanying drawing figureswherein:

FIGS. 1A and 1B depict a side view and a cross-sectional view,respectively, of a spatially-selective reflective structure according toone embodiment of the invention.

FIG. 1C depicts a reflecting disk with a plurality of modulationsarranged in a single-turn spiral according to one embodiment of theinvention.

FIGS. 2A-2F depict several modulation profiles according to someembodiments of the invention.

FIG. 3A depicts an imaging system incorporating a spatially-selectivereflective structure according to one embodiment of the invention.

FIG. 3B depicts an imaging system incorporating a spatially-selectivereflective structure and radar absorbing material according to oneembodiment of the invention.

FIG. 3C depicts an imaging system incorporating a spatially-selectivereflective structure and a beam splitter according to one embodiment ofthe invention.

FIG. 3D depicts an imaging system incorporating a spatially-selectivereflective structure and secondary optics according to one embodiment ofthe invention.

FIGS. 4A-4C depict the acquisition of an image according to oneembodiment of the invention.

FIG. 5 depicts an imaging method according to one embodiment of theinvention.

FIG. 6A depicts a three layer model for reflectivity of thespatially-selective reflective structure according to one embodiment ofthe invention.

FIG. 6B depicts reflection coefficient Γ as a function of gap distance,partially-conductive slab thickness, and partially-conductive slabconductivity.

FIG. 7 depicts an embodiment of a modulating reflector disk including aplurality of randomly-positioned modulations.

FIG. 8 depicts an exaggerated modulating reflector disk and a nine-pixelviewing window.

FIG. 9 depicts a method of creating a multi-pixel image according to oneembodiment of the invention.

FIG. 10 depicts a partially-conducting slab including a non-conductivematerial coated with a thin metallic film according to one embodiment ofthe invention.

FIGS. 11A-11C depict schematics for reflective structures havingdepressions, bumps, and no modulations, respectively, according tovarious embodiments of the invention.

FIGS. 12A-12I depict the power reflectivity coefficient as function ofreflector distance and/or sheet resistance for various radiationincidence angles according to various embodiments of the invention.

FIGS. 13A and 13B depict the power reflection profile of aspatially-selective reflective structure having a depression of lineardimensions 2λ and 3λ, respectively, for a reflective structure whereinthe depression distance and reflector distance from the resistive sheetare

${\frac{\lambda}{2}{\mspace{11mu}\;}{and}\mspace{14mu}\frac{\lambda}{4}},$respectively, the sheet resistivity is 377Ω/□, and the radiation isnormally incident to the structure according various embodiments of theinvention.

FIGS. 14A and 14B depict the power reflection profile of aspatially-selective reflective structure having a bump distance andreflector distance of

${\frac{\lambda}{2}{\mspace{11mu}\;}{and}\mspace{14mu}\frac{3\lambda}{4}},$respectively, a sheet resistivity of 377Ω/□, and radiation normallyincident to the structure according to various embodiments of theinvention

FIG. 15 depicts the power reflection coefficient for a structure that ismodulated by two depressions separated by a gap that varies from 0.1λ to10λ according to various embodiments of the invention.

FIGS. 16A, 16B, 16C, and 16D depict slices of FIG. 15 and providereflectivity profiles for separations of 4λ, 4.5λ, 5λ, and 10λ,respectively, according to various embodiments of the invention.

FIG. 17 depicts a method of fabricating a reflector disk according toone embodiment of the invention.

FIG. 18 depicts the fabrication of a reflector disk according to oneembodiment of the invention.

FIGS. 19A and 19B depict spatially-selective reflector device and motorassemblies according to various embodiments of the invention.

FIG. 20 depicts a method for calculating a measurement matrix accordingto an embodiment of the invention.

FIG. 21 depicts a profiling scanner incorporating the imaging devicesdescribed herein according to an embodiment of the invention.

DESCRIPTION OF THE INVENTION

Spatially-selective reflective structures are described along withsystems and methods utilizing spatially-selective reflective structures.The spatially-selective reflective structures can be used to imagetargets using electromagnetic energy of a various wavelengths referredto herein as the “wavelength(s) of interest.”

Spatially-Selective Reflective Structures

FIGS. 1A and 1B depict a side view and a cross-sectional view,respectively, of a spatially-selective reflective structure 100according to one embodiment of the invention. Spatially-selectivereflective structure 100 includes a partially-conducting slab 102 and amodulating reflector disk 104. The modulating reflector disk 104includes a plurality of modulations 106 a-h.

Modulations 106 a-h are preferably uniform in size and shape. Themodulations can be designed to maximally perturb the absorptionproperties of the partially-conducting slab 102 and reflector disk 104.Preferably, the modulations have well-defined edges, as depicted in FIG.1A, which promote energy reflection. While particular sizes and shapesare not required, exemplary modulations can, in some embodiments, have across-sectional dimension greater or equal to about one wavelength ofinterest and extend above or below the surface of modulating reflectordisk 104.

The height or depth of the modulations 106 is generally about less thana wavelength of interest or a multiple of a half of one wavelength ofinterest plus about less than a half of one wavelength of interest. Forexample, modulation height H can be defined by the following formula:

$\begin{matrix}{H \approx {{n_{m}\frac{\lambda}{2}} + {d_{m}\frac{\lambda}{2}}}} & (1)\end{matrix}$wherein n_(m) is a non-negative integer, λ is the wavelength ofinterest, and 0≦d_(m)≦1. Parameter d_(m) will vary depending on theproperties of the partially-conducting slab 102 (e.g. the thickness ofthe slab 102, the electrical conductivity of the slab 102, and theelectrical permittivity of the slab 102). For example, if a slab 102 isprovided with a uniform electrical conductivity of 0.066 S/cm, thicknessof 820 μm, and relative electrical permittivity of 11.9 F/m, and thefrequency of interest is 640 GHz (λ=468.75 μm), the desired bump heightH_(b) (i.e., the distance from surface of the partially-conducting slabz₂ to the surface of bump z_(3a) as depicted in FIG. 6A) for maximalreflection of radiation can be defined as follows:

$\begin{matrix}{H_{b} \approx {{n_{m}\frac{\lambda}{2}} + {\frac{47}{2}\mu\; m}} \approx {{n_{m}\frac{\lambda}{2}} + {0.1{\frac{\lambda}{2}.}}}} & (2)\end{matrix}$The desired depression depth H_(d) (i.e., the distance from the surfaceof the partially-conducting slab to the depression surface) for maximalreflection of radiation for the such a slab can be defined as follows:

$\begin{matrix}{H_{d} \approx {{n_{m}\frac{\lambda}{2}} + {\frac{347}{2}\mu\; m}} \approx {{n_{m}\frac{\lambda}{2}} + {0.4{\frac{\lambda}{2}.}}}} & (3)\end{matrix}$

The partially-conducting slab 102 can be composed of a semiconductormaterials including but not limited to: diamond, silicon, germanium,silicon carbide, silicon germanide, aluminum antimonide, aluminumarsenide, aluminum nitride, aluminum phosphide, boron nitride, boronphosphide, boron arsenide, gallium antimonide, gallium arsenide, galliumnitride, gallium phosphide, indium antimonide, indium arsenide, indiumnitride, indium phosphide, aluminum gallium arsenide, indium galliumarsenide, indium gallium phosphide, aluminum indium arsenide, aluminumindium antimonide, gallium arsenide nitride, gallium arsenide phosphide,aluminum gallium nitride, aluminum gallium phosphide, indium galliumnitride, indium arsenide antimonide, indium gallium antimonide, aluminumgallium indium phosphide, aluminum gallium arsenide phosphide, indiumgallium arsenide phosphide, aluminum indium arsenide phosphide, aluminumgallium arsenide nitride, indium gallium arsenide nitride, indiumaluminum arsenide nitride, gallium arsenide antimonide nitride, galliumindium nitride arsenide antimonide, gallium indium arsenide antimonidephosphide, cadmium selenide, cadmium sulfide, cadmium telluride, zincoxide, zinc selenide, zinc sulfide, zinc telluride, cadmium zinctelluride, mercury cadmium telluride, mercury zinc telluride, mercuryzinc selenide, cuprous chloride, lead selenide, lead sulfide, leadtelluride, tin sulfide, tin telluride, lead tin telluride, thallium tintelluride, thallium germanium telluride, bismuth telluride, cadmiumphosphide, cadmium arsenide, cadmium antimonide, zinc phosphide, zincarsenide, zinc antimonide, lead(II) iodide, molybdenum disulfide,gallium selenide, tin sulfide, bismuth sulfide, copper indium galliumselenide, platinum silicide, bismuth(III) iodide, mercury(II) iodide,thallium(I) bromide, titanium dioxide (anatase), copper(I) oxide,copper(II) oxide, uranium dioxide, and uranium trioxide. Thepartially-conducting slab 102 can be composed of one or more organicsemiconductors. The partially-conducting slab 102 and magneticsemiconductors such as magnetite, manganese-doped indium arsenide,manganese-doped gallium arsenide, manganese-doped indium antimonide,manganese- and iron-doped indium oxide, manganese-doped zinc oxide,n-type cobalt-doped zinc oxide, cobalt-doped titanium dioxide,chromium-doped rutile, iron-doped rutile, iron-doped anatase,nickel-doped anatase, manganese-doped tin dioxide, and iron-doped tindioxide.

The partially-conducting slab 102 can additionally or alternatively be adielectric loaded with conductive particles, such as ions, silver, gold,copper, aluminum, platinum, iron, carbon black, and alloys thereof. Theconductive particles can be introduced into the dielectric in a mannersimilar to semiconductor doping techniques.

The partially-conducting slab 102 can be a non-conductive materialcoated with a thin metal film, such as silver, gold, copper, aluminum,platinum, iron, and alloys thereof. The film can be applied with coatingtechniques such as physical vapor deposition (PVD) or chemical vapordeposition (CVD). It will be appreciated by one of skill in the art thatmany other methods can be used and that certain methods may beadvantageous for particular coatings and/or non-conductive materials.

The thin metal film can be any film thinner than the wavelength ofinterest. In some embodiments, the thin metal coating is less than about10 angstroms thick. In some embodiments, the thin metal film can have aresistivity of about 377Ω/□, particularly where the radiation angle ofincidence is less than 20° from the normal of the structure. Thin metalfilms with other resistivities can also be utilized depending on thespecifications of the device. For example, the resistivity can bebetween about 225Ω/□, about 250Ω/□, about 275Ω/□, about 300Ω/□, about325Ω/□, about 350Ω/□, about 375Ω/□, about 400Ω/□, about 425Ω/□, about450Ω/□, about 475Ω/□, about 500Ω/□, about 525Ω/□, about 550Ω/□, about575Ω/□, and the like.

In some embodiments, the partially-conducting slab has a uniformconductivity profile value of about 0.066 Siemens per centimeter (S/cm).

In some embodiments, the modulating reflector disk 104 is composed of ametal. The metal can, in some embodiments, be a highly-conductive metalsuch as copper, silver, and aluminum.

The partially-conducting slab 102 and the modulating reflector disk 104can be separated by a gap 108 and can be coupled with one or moremechanical fasteners 110 a-d, such as screws, bolts, nails, rivets, andthe like. For example, the fasteners 110 a-d can be bolts or screwscoupled with one or more spacers such as washers. One or more of thewashers can be selectively removed to adjust the gap 108. The gap 108need not be devoid of any material. Rather, the gap 108 can be open tothe atmosphere. In other embodiments, the partially-conducting slab 102and the modulating reflector disk 104 are bonded with a submillimeterwavelength transparent adhesive that functions as a gap 108.

In other embodiments, the partially-conducting slab 102 and themodulating reflector disk 104 can be free of each other. The modulatingreflector disk 104 can be rotated while it is kept parallel to thepartially-conducting slab 102.

The gap 108 can be configured to achieve maximal absorption of incidentelectro-magnetic radiation at submillimeter wavelengths. In someembodiments (e.g., embodiments in which the gap G is air), the gap G isdefined as

$\begin{matrix}{G \approx {{n_{g}\frac{\lambda}{2}} + {d_{g}\frac{\lambda}{2}}}} & (4)\end{matrix}$wherein n_(g) is a non-negative integer, λ is the wavelength ofinterest, and 0≦d_(g)≦1. Parameter d_(g) will vary depending on theproperties of the partially-conducting slab 102. The properties of thepartially-conducting slab 102 affecting d_(g) are the thickness of theslab 102, the electrical conductivity of the slab 102, and theelectrical permittivity of the slab 102. For example, if a slab 102 isprovided with a uniform electrical conductivity of 0.066 S/cm, thicknessof 820 μm, and relative electrical permittivity of 11.9 F/m, and thefrequency of interest is 640 GHz (λ=468.75 μm), the desired gap Gbetween the plates for maximal absorption of radiation can be expressedas follows:

$\begin{matrix}{G \approx {{n_{g}\frac{\lambda}{2}} + \frac{78}{2}} \approx {{n_{g}\frac{\lambda}{2}} + {0.16{\frac{\lambda}{2}.}}}} & (5)\end{matrix}$Parameters n_(g) and n_(m) can, but need not necessarily equal eachother modulations when the modulations are depressions, but arepreferably different when the modulations are bumps. d_(g) and d_(m) arepreferably different in either case. Parameters n_(g) and n_(m) arepreferably as small as possible, particularly where the modulations aredepressions.

In other embodiments in which the partially-conducting slab 102 is madeof a non-conductive material coated with a thin metal film on the sideadjacent to the reflecting disk 104, the gap 108 can be about one oddmultiple of a quarter of a wavelength of the energy to be detected. Forexample, if the wavelength to be detected is about 2,800 μm, the gap 108can be about 700 μm (if the modulations are depressions), about 2,100μm, about 3,500 μm, and so on.

In some embodiments, the modulations 106 are arranged in a single-turnspiral starting from an external radial point of the reflecting disk 104and proceeding to the center of the disk 104 in a manner similar to agramophone record. In order to minimize the curvature of scan lines, alarge disk 104 can be used with small modulations 106 located closer tothe perimeter of the disk. An example of such a disk is depicted in FIG.1C.

As depicted in FIGS. 2A-H, modulations 206 can be either bumps (206 a,206 b, 206 c) or depressions (206 d, 206 e, 206 f). Modulations 206 canbe any shape including a cylinder (206 a, 206 d), a cuboid (206 b, 206e), and right triangular prism (206 c, 206 f). The shape of modulation206 may have a diminishing effect on the quality or quantity ofreflections as the modulations decrease in size. The face of themodulations 206 are preferably parallel to the face ofpartially-conductive slab 102 and modulating reflector disk 104.

The spatially-selective reflective structure 100 provided herein isparticularly useful for submillimeter imaging and other imagingtechniques where the resolution of existing imagers is constrainedeither by technology or cost.

Imaging Systems

FIG. 3A depicts a system 300 incorporating a spatially-selectivereflective structure 302. A submillimeter wave source 304 emitsradiation at a desired wavelength. Submillimeter wave source 304 exposesobject of interest 306 with submillimeter waves, which are reflected tosubmillimeter optics 308. Focusing mirror 308 directs the reflection tospatially-selective reflective structure 302. As spatially-selectivereflective structure 302 is spun by motor 310, modulations 312 areindividually brought into the focal plane of focusing minor 308 andreflect the submillimeter wave to submillimeter receiver 314.

Submillimeter radiation (also known as “terahertz radiation”, “terahertzwaves”, “terahertz light”, “T-rays”, “T-light”, “T-lux”, and “THz”) isgenerally used to describe the region of the electromagnetic spectrumbetween about 300 gigahertz (3×10¹¹ Hz) and about 3 terahertz (3×10¹²Hz), which corresponds to wavelength ranges between about 1 millimeterand about 100 micrometers. Submillimeter radiation can be produced bydevices such as gyrotrons, backward wave oscillators (BWOs), farinfrared lasers (FIR lasers), quantum cascade lasers, free electronlasers (FELs), synchrotron light sources, and photomixing devices.

Gyrotrons are available from Communications & Power Industries of PaloAlto, Calif.; Gyrotron Technology, Inc. of Bensalem, Pa.; Thales Groupof Neuilly-sur-Seine, France; and Toshiba Corporation of Tokyo, Japan.Backward wave oscillators are described in U.S. Pat. No. 2,880,355. Farinfrared lasers are available from Zaubertek, Inc. of Oviedo, Fla.,Laser 2000 GmbH of Munich, Germany, and Coherent, Inc. of Santa Clara,Calif. Quantum cascade lasers are described in U.S. Pat. Nos. 7,359,418and 7,386,024 and U.S. Patent Application Publication Nos. 2008/0069164and 2008/0219308. Free electron lasers are described in U.S. Pat. No.7,342,230. Synchrotron light sources are available from LynceanTechnologies, Inc. of Palo Alto, Calif. Photomixing devices aredescribed in U.S. Pat. Nos. 7,105,820 and 7,326,930 and U.S. PatentApplication Publication Nos. 2005/0156110; 2006/0054824; and2007/0229937. Integrated submillimeter generators and detectors areavailable under the PICOMETRIX® T-RAY™ trademark from Advanced Photonix,Inc. of Ann Arbor, Mich.

Submillimeter optics 308 can include one or more focusing mirrors (alsoknown as “concave mirrors”) are available from suppliers such as EdmundOptics Inc. of Barrington, N.J. Focusing minors can composed of glass,metal, or other materials capable of reflecting submillimeter radiation.Suitable mirrors (e.g. gold-coated aluminum substrates) are availablefrom RadiaBeam Technologies, LLC of Marina Del Ray, Calif.

Motor 310 spins at a speed sufficient to produce a desired number offrames per minute. For example, if the receiver 314 is to capture imagesat a rate of 30 frames per second, motor 310 can spinspatially-selective reflective structure 302 at a rate of 1,800revolutions per minute. Motor 310 can, in some embodiments, be aservomechanical device capable of actuation to defined rotationalpositions and/or capable of self-correction of deviations from a desiredrotational position and/or speed.

Imaging Methods

Referring to FIGS. 4A-4C, an image of object 306 (in this example, aknife) is acquired by submillimeter receiver 314 from aspatially-selective reflective structure 302, e.g. a spatially-selectivereflective structure including a modulating reflector disk 104 asdepicted in FIG. 1C. Receiver 314 focuses on a viewing window 402 on thespatially-selective reflective structure 302. Viewing window 402 can bea physical opening in a absorptive material or can be a region that thereceiver 314 focuses on while the spatially-selective reflectivestructure 302 rotates through the viewing window 402. The absorptivematerial can be positioned adjacent to the partially-conductive slab 102or receiver 314 and is preferably positioned as close to thepartially-conductive slab as possible. Suitable absorptive materialsinclude ECCOSORB® materials (available from Emerson & Cuming ofRandolph, Mass.) and radar absorbent materials (RAM).

As the spatially-selective reflective structure 302 rotates, themodulation 106 a on the outer radius of the spiral enters the viewingwindow 402. The energy reflected from the modulation is recorded as themodulation 106 a moves across the window. The recorded data isrepresented and stored as a function of the modulation position, asdepicted as element 404 a in FIGS. 4A-4C. The process continues withmodulations 106 b, 106 c, 106 d, 106 e, 106 f, 106 g, 106 h to imagerows 404 b, 404 c, 404 d, 404 e, 404 f, 406 g, 404 h, respectively. Atthis point, modulation 106 a reenters the viewing window 402 and theprocess is repeated to capture another image.

FIG. 5 depicts an imaging method according to one embodiment of theinvention. In step S502, an imaging device is provided, for example animaging device described herein. The imaging device can includesubmillimeter wave optics, a spatially-selective reflective structure, amotor configured to rotate the spatially-selective reflective structure,and a submillimeter wave receiver as described herein. In step S504, themotor is actuated to rotate the spatially-selective reflectivestructure. In step S506, a plurality of reflections are captured by thesubmillimeter wave receiver. In step S508, each reflection is stored asa pixel. In step S510, an image is formed from a plurality of pixels.

In step S512, the image can be processed with an image recognitionmethod capable of identifying suspicious items that could be a weapon orcontraband. Various suitable methods are known to those of skill in theart and include edge detection algorithms and artificial intelligencealgorithms (e.g. neural nets) such as those described in U.S. Pat. Nos.7,310,442 and 7,417,440 and U.S. Patent Application Publication No.2008/0212742 and in Mohamed-Adel Slamani et al., “Image Processing Toolsfor the Enhancement of Concealed Weapon Detection,” 3 Proc. Int'l Conf.on Image Processing 518-22 (October 1999). One or more privacyalgorithms can also be applied to the images to obscure sensitiveregions such as human genitalia.

In step S514, the image can be stored either by dedicated hardware orsoftware or by a general purpose computer programmed to acquire, store,display, and/or transmit the images.

The images can be stored in variety of formats including known andproprietary vector graphics formats such as vector graphics formats andraster graphics formats. Vector graphics (also called geometric modelingor object-oriented graphics) utilize geometrical primitives such aspoints, lines, curves, and polygons to represent images. Examples ofvector graphics formats include the Scalable Vector Graphics (SVG) andVector Markup Language (VML) formats. The SVG format is defined at W3C,Scalable Vector Graphics (SVG), http://www.w3.org/Graphics/SVG/. VML isdescribed in Brian Matthews, et al., Vector Markup Language (VML),http://www.w3.org/TR/1998/NOTE-VML-19980513. Alternatively, the imagescan be converted to or maintained in a raster graphics format, which isa representation of images as a collection of pixels. Examples of rastergraphics formats include JPEG, TIFF, RAW, PNG, GIF, and BMP.

The images can also be compiled into a video format such as BETAMAX®,BLU-RAY DISC®, DVD, D-VHS, Enhanced Versatile Disc (EVD), HD-DVD,Laserdisc, M-JPEG, MPEG-1, MPEG-2, MPEG-4, Ogg-Theora, VC-1, VHS, andthe like.

Image and/or video files can be stored on media such as magnetic media(e.g. tapes, discs), optical media (e.g. CD-ROM, CD-R, CD-RW, DVD, HDDVD, BLU-RAY DISC®, Laserdisc), punch cards, and the like. Image and/orvideo files can also be transmitted to a remote storage device by avariety of standards such as parallel or serial ports, Universal SerialBus (USB), USB 2.0, Firewire, Ethernet, Gigabit Ethernet, and the like.

In step S516, the images or video can be displayed on a display devicesuch as a cathode ray tube (CRT), a plasma display, a liquid crystaldisplay (LCD), an organic light-emitting diode display (OLED), alight-emitting diode (LED) display, an electroluminescent display (ELD),a surface-conduction electron-emitter display (SED), a field emissiondisplay (FED), a nano-emissive display (NED), an electrophoreticdisplay, a bichromal ball display, an interferometric modulator display,a bistable nematic liquid crystal display, and the like.

In step S518, images can also be printed with devices such laserprinters, ink jet printers, dot matrix printers and the like.

As one will appreciate, the steps of the methods described herein can beconfigured to place various steps in various orders and may includeadditional steps or omit steps listed in FIG. 5. Specifically, one ofskill in the art will realize that image handling steps S512, S514,S516, and S518 can be practiced various orders and/or combinations.

Optimization of Spatially-Selective Reflective Structures

Referring now to FIG. 6, the reflectivity of a spatially reflectivestructure can be represented with a three layer model 600. Radiationfrom source 602 (e.g. reflections from an object of interest), passesthrough the air (E1), partially-conducting slab (E2), and gap (E3),before reflecting off the modulating reflector disk 104 before passingthrough partially-conducting slab (E2) and air (E1) and being imaged byimager 604. The electric field for each layer (E1, E2, E3) can beexpressed in the following matrices, where E_(i) ^(±) is the electricfield in the i^(th) layer and the plus or minus sign indicates thedirection of propagation as depicted in FIG. 6:

$\begin{matrix}{{\begin{bmatrix}{\mathbb{e}}^{{j\gamma}_{1}z_{1}} & {- {\mathbb{e}}^{{- {j\gamma}_{2}}z_{1}}} & {- {\mathbb{e}}^{{j\gamma}_{2}z_{1}}} & 0 & 0 \\{- \frac{{\mathbb{e}}^{{j\gamma}_{1}z_{1}}}{\eta_{1}}} & {- \frac{{\mathbb{e}}^{{- {j\gamma}_{2}}z_{1}}}{\eta_{2}}} & \frac{{\mathbb{e}}^{{j\gamma}_{2}z_{1}}}{\eta_{2}} & 0 & 0 \\0 & {\mathbb{e}}^{{- {j\gamma}_{2}}z_{2}} & {\mathbb{e}}^{{j\gamma}_{2}z_{2}} & {- {\mathbb{e}}^{{- {j\gamma}_{3}}z_{2}}} & {- {\mathbb{e}}^{{- {j\gamma}_{3}}z_{2}}} \\0 & \frac{{\mathbb{e}}^{{- {j\gamma}_{2}}z_{2}}}{\eta_{2}} & {- \frac{{\mathbb{e}}^{{j\gamma}_{2}z_{2}}}{\eta_{2}}} & {- \frac{{\mathbb{e}}^{{- {j\gamma}_{3}}z_{2}}}{\eta_{3}}} & \frac{{\mathbb{e}}^{{j\gamma}_{3}z_{2}}}{\eta_{3}} \\0 & 0 & 0 & {\mathbb{e}}^{- {j\gamma 3z}_{3}} & {\mathbb{e}}^{{j\gamma}_{3}z_{3}}\end{bmatrix}\left\lbrack \begin{matrix}E_{1}^{-} \\E_{2}^{+} \\E_{2}^{-} \\E_{3}^{+} \\E_{3}^{-}\end{matrix} \right\rbrack} = {\quad\begin{bmatrix}{{- E_{1}^{+}}{\mathbb{e}}^{{- {j\gamma}_{1}}z_{1}}} \\{{- \frac{E_{1}^{+}}{\eta_{i}}}{\mathbb{e}}^{{- {j\gamma}_{1}}z_{1}}} \\0 \\0 \\0\end{bmatrix}}} & (6)\end{matrix}$The variable z_(i) is the thickness of the layer.

The complex propagation constants for each layer are given by theformula γ_(i)=α_(i)+β_(i) with

$\begin{matrix}{\alpha_{i} = {\omega\left\{ {\frac{\mu_{i}ɛ_{i}^{\prime}}{2}\left\lbrack {\sqrt{1 + \frac{ɛ_{i}^{\prime\prime}}{ɛ_{i}^{\prime\prime}}} - 1} \right\rbrack} \right\}^{2}}} & \left( {7a} \right)\end{matrix}$and

$\begin{matrix}{\beta_{i} = {\omega{\left\{ {\frac{\mu_{i}ɛ_{i}^{\prime}}{2}\left\lbrack {\sqrt{1 + \frac{ɛ_{i}^{\prime\prime}}{ɛ_{i}^{\prime\prime}}} + 1} \right\rbrack} \right\}^{2}.}}} & \left( {7b} \right)\end{matrix}$The impedance for each layer is given by

$\begin{matrix}{\eta_{i} = {\sqrt{\frac{\mu_{i}}{ɛ_{i}^{\prime}}}{\left( {1 - {j\frac{ɛ_{i}^{\prime\prime}}{ɛ_{i}^{\prime}}}} \right)^{\frac{1}{2}}.}}} & (8)\end{matrix}$

In equations (7) and (8), ε_(i)′≡ε_(i) (the dielectric permittivity oflayer i) and

$ɛ_{i}^{\prime\prime} \equiv \frac{\sigma_{i}}{\overset{\_}{\omega}}$where σ_(i) is the conductivity of the layer. The radial frequency isgiven by ω=2πf where f is the frequency of the terahertz field. Thelayers are assumed to be non-magnetic, so that μ_(i)=μ₀, which is themagnetic permeability of free space.

Matrix equation (6) can be easily solved with the help of numericalcomputing software such as MATLAB®, available from The MathWorks ofNatick, Mass., MAPLE®, available from Waterloo Maple, Inc. of Waterloo,Ontario, and the like. The reflection coefficient Γ can be obtained fromthe ratio

$\Gamma = {{\frac{E_{1}^{-}}{E_{1}^{+}}}.}$

FIG. 6B depicts reflection coefficient Γ as a function of gap distance(i.e. z₃-z₂), partially-conductive slab thickness (i.e. z₂-z₁), andpartially-conductive slab conductivity. FIG. 6B(i) depicts reflectioncoefficient Γ as a function of reflector distance for a slab withconductivity 0.066 S/cm and thickness 820 μm. FIG. 6B(ii) depictsreflection coefficient Γ as a function of slab thickness for a slab withconductivity 0.066 S/cm and reflector distance of 1440 μm. FIG. 6B(iii)depicts reflection coefficient Γ as a function of slab conductivity fora slab of thickness 820 μm and reflector distance of 1440 μm.

As discussed herein, modulation height is preferably selected formaximal reflection of radiation while gap G is preferably selected formaximal absorption of radiation. These values can be identified byselecting a local maxima in FIG. 6B(i) for the modulation height ordepth and selecting a local minima in FIG. 6B(i) for the gap value. Ingenerally, optimal modulation heights approximate multiples of one-halfof the wavelength of energy to be detected.

Further Reflector Disks

Referring now to FIG. 7, another embodiment of a modulating reflectordisk 704 is depicted. Modulating reflector disk 704 includes a pluralityof modulations 706 that are arranged in such a manner that as the disk704 is rotated the orientation of modulations 706 produces a matrixhaving linearly independent rows as discussed herein, thus ensuring thatthe inverse of the matrix exists. Although random placement of pixelswill almost always produce such an arrangement, the arrangement ofmodulations can be produced by a human or by a computer algorithm.

In order to utilize modulating reflector disk 704, receiver 314 focuseson a viewing window 702 as discussed above in the context of FIGS. 3 and4 herein. However, instead of defining viewing window 702 to encompass asingle modulation at any given time as in FIG. 4, viewing window 702 canencompass a plurality of modulations 706.

In order to permit a low resolution receiver 314 (e.g., a single-pixelimager such as a submillimeter antenna) to capture multi-pixel images,viewing window 702 is divided into a plurality of arbitrary,non-physical pixels 708.

FIG. 8 depicts an exaggerated disk 804 and a viewing window 802 havingnine pixels p₁-p₉ in order to depict an imaging method 900 described inFIG. 9. In step S902, an imaging device is provided (e.g., an imagingdevice as described herein). As the disk 804 is rotated (S904), receiver314 takes a number of measurements equal to the number of arbitrarypixels in viewing window 802 (S906). For example, in the nine-pixelembodiment depicted in FIG. 8, receiver 314 can take a measurement at40° increments of rotation of disk 804.

Measurements need not occur at regular intervals and need not encompassa complete revolution of disk 804. For example, in the nine-pixelembodiment depicted in FIG. 8, receiver 314 can take measurements at 10°increments of rotation of disk 804 to obtain four 3×3 images. In such anembodiment, measurements at 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, and80° are used to produce a first image; measurements at 90°, 100°, 110°,120°, 130°, 140°, 150°, 160°, and 170° are used to produce a secondimage; measurements at 180°, 190°, 200°, 210°, 220°, 230°, 240°, 250°,and 260° are used to produce a third image; and measurements at 270°,280°, 290°, 300°, 310°, 320°, 330°, 340°, and 350° are used to produce afourth image.

The measurements used to generate consecutive images can overlap. Forexample, if one seeks to obtain a plurality of 18×18 pixel images, 324measurements are required for each image. If measurements are obtainedat 1° increments, the first image can be obtained from measurements from0° to 323°, the second image can be obtained from measurements from 324°of the first revolution to 286° of the second revolution, and so on.

Although it is possible to obtain series of images that are eachcaptured at a unique set of rotational positions, it may be preferablein some embodiments to capture each image at the same set of rotationalpositions (e.g., 1° increments from 0° to 323° on each revolution) inorder to minimize processing and storage requirements by only storing asingle, pre-calculated measurement matrix (see equation 10) and itsinverse (see equation 11).

In order to produce a multi-pixel image, the fraction of the each pixelarea that is backed by a modulation is calculated for each rotationalposition at which a measurement will be taken. For example, at therotational position depicted in FIG. 8, 40% of pixel p₁, 15% of pixelp₂, 55% of pixel p₃, 22% of pixel p₄, 20% of pixel p₅, 8% of pixel p₆,43% of pixel p₇, 36% of pixel p₈, and 70% of pixel p₉ are backed by oneor more modulations. At this first position, a measurement m₁ is taken.This measurement m₁ will reflect the signal reflected onto receiver 314by the portion of viewing window 802 that is backed by modulations asreflected in equation (9) below.m ₁=0.4p ₁+0.15p ₂+0.55p ₃+0.22p ₄+0.2p ₅+0.08p ₆+0.43p ₇+0.36p ₈+0.7p₉  (9)This equation can be solved as part of a system of linear equationsalong with the equations obtained at other rotational positions (S908).These equations can be expressed in matrix form as shown in equation(10) below wherein dots (.) represent the coefficients in front ofpixels p₁-p₉ for the other positions of the disk 804 and m₁-m₉ representthe corresponding measured signal for each position. As will beappreciated by one of skill in the art, the rows of the matrix arepreferably independent of each other, so that the system of linearequations can be solved.

The 9×9 matrix in equation (10) is the measurement matrix mentionedpreviously. For an image with n pixels, the measurement matrix will havedimensions of n×n.

$\begin{matrix}{{\begin{bmatrix}0.4 & 0.15 & 0.55 & 0.22 & 0.2 & 0.08 & 0.43 & 0.36 & 0.7 \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots\end{bmatrix} \times \begin{bmatrix}p_{1} \\p_{2} \\p_{3} \\p_{4} \\p_{5} \\p_{6} \\p_{7} \\p_{8} \\p_{9}\end{bmatrix}} = {\quad\begin{bmatrix}m_{1} \\m_{2} \\m_{3} \\m_{4} \\m_{5} \\m_{6} \\m_{7} \\m_{8} \\m_{9}\end{bmatrix}}} & (10)\end{matrix}$The matrix equation can be solved for values p₁-p₉ as shown in equation(11) below:

$\begin{matrix}{\begin{bmatrix}p_{1} \\p_{2} \\p_{3} \\p_{4} \\p_{5} \\p_{6} \\p_{7} \\p_{8} \\p_{9}\end{bmatrix} = {\begin{bmatrix}0.4 & 0.15 & 0.55 & 0.22 & 0.2 & 0.08 & 0.43 & 0.36 & 0.7 \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots & \ldots\end{bmatrix}^{- 1} \times {\quad\begin{bmatrix}m_{1} \\m_{2} \\m_{3} \\m_{4} \\m_{5} \\m_{6} \\m_{7} \\m_{8} \\m_{9}\end{bmatrix}}}} & (11)\end{matrix}$

The values p₁-p₉ can be used to generate a multi-pixel image (S910). Forexample, values p₁-p₉ can be mapped to grayscale values to produce agrayscale image. Alternatively, values p₁-p₉ can be mapped to black orwhite to produce a black-and-white image.

The image can then be processed (S912), stored (S914), displayed (S916),and/or printed (S918) as discussed herein.

As will be appreciated by one of skill in the art, the systems andmethods described herein can be scaled to produce images larger than theexamples described herein. For example, to produce a 100×100 pixelimage, 10,000 measurements are obtained (corresponding to 10,000distinct modulation patterns). These measurements can be obtained bytaking a measurement every 0.036° (360°/10000).

Additional Imaging Systems

In some embodiments of the invention, an imaging system (e.g., theimaging system described in the context of FIG. 3A herein) is configuredto prevent radiation reflected by the object of interest 306 fromdirectly entering receiver 314. A variety of approaches can be utilizedto achieve this goal.

In one embodiment, the receiver 314 includes a highly-directive antennadirected toward the imaging window on the spatially selective mirror sothat energy received directly from the object of interest 306 isseverely attenuated.

In another embodiment depicted in FIG. 3B, a blocking mask ofradar-absorbing material (RAM) 316 can be placed around the receiver 314to prevent external radiation from reaching the receiver 314.

In still another embodiment depicted in FIG. 3C, a beam splitter 318allows for the positioning of receiver 314 away from the likely path ofambient energy reflected by object of interest 306.

In some embodiments, the imaging system is designed for “standoff”detection, for example, from a distance of about 5 to 50 meters from anobject of interest. However, embodiments of the invention herein can beconfigured to scan objects of interest at ranges of less than 5 metersor greater than 50 meters from an object of interest. For example, asdepicted in FIG. 3D, an imaging system can include one or more secondaryoptics 318 a, 318 b (e.g., optics having aplanatic surfaces). Thesecondary optics 318 can be movable in order to focus the imaging system300 d

Optimization of Partially-Conducting Slabs

As discussed herein and depicted in FIG. 10, in some embodiments,partially-conducting slab 1002 can be a non-conductive material 1012coated with a thin metallic film 1014. This embodiment of thepartially-conducting slab 1002 is also referred to herein as a“resistive sheet.”

The optimal parameters for the distance of the modulations and theresistive sheet 1002 can be expressed by the formula in the context ofFIGS. 11A-11C:

$\begin{matrix}{{{d_{n} = {n\frac{\lambda}{2\sqrt{ɛ_{r}{\cos\left( \phi_{i} \right)}}}}},{n = 1},2,\ldots}\mspace{31mu}} & (12)\end{matrix}$where ε_(r) is the relative permittivity of the media between the thinmetallic layer 1014 and the modulation 1006, λ is the wavelength ofinterest, and φ_(i) is the angle of radiation incidence given withrespect to the normal of the spatially-selective minor 1000.

Similarly, the optimal distance for absorption (i.e., the distancebetween the metallic layer 1014 and the area of reflector disk 1004without a modulation 1006) can be expressed by the formula:

$\begin{matrix}{{{d_{r} = \frac{\left( {{2n} - 1} \right)\lambda}{4\sqrt{ɛ_{r}}{\cos\left( \phi_{i} \right)}}},{n = 1},2,\ldots}\mspace{31mu}} & (13)\end{matrix}$

The optimal value of the resistivity depends on the angle of incidenceφ_(i). FIGS. 12A-12I depict the results of a method of moments analysisto calculation the reflectivity of a structure similar to the structuredepicted in FIG. 11C.

FIGS. 12A-12C depict the power reflectivity coefficient as a function ofreflector distance and/or sheet resistivity for radiation normallyincident to the structure. FIG. 12A depicts the log₁₀ of thereflectivity as a function of reflector distance (x-axis) and the sheetresistivity (y-axis). FIGS. 12B and 12C depict slices through the linesin FIG. 12A, but are displayed linearly (i.e., not in log₁₀).

FIGS. 12D-12F depict the power reflectivity coefficient as a function ofreflector distance and/or sheet resistivity for radiation incident tothe structure at 10° off the normal. FIG. 12D depicts the log₁₀ of thereflectivity as a function of reflector distance (x-axis) and the sheetresistivity (y-axis). FIGS. 12E and 12F depict slices through the linesin FIG. 12D, but are displayed linearly (i.e., not in log₁₀).

FIGS. 12G-12I depict the power reflectivity coefficient as a function ofreflector distance and/or sheet resistivity for radiation incident tothe structure at 20° off the normal. FIG. 12G depicts the log₁₀ of thereflectivity as a function of reflector distance (x-axis) and the sheetresistivity (y-axis). FIGS. 12H and 12I depict slices through the linesin FIG. 12G, but are displayed linearly (i.e., not in log₁₀).

As depicted in FIGS. 12A-12I, the optimal parameters change with theangle of incidence. The distance parameters as a function of radiationincidence angle are given by equations (12) and (13) and sheetresistivity can be maintained at approximately that of free space (i.e.,about 377Ω/□) for angles of incidence less than about 20°.

Additionally, as depicted in FIGS. 12A-12I, the dynamic range of thereflector (minimum to maximum reflectivity range) is larger if theradiation is normally incident on the structure. In this regard,embodiments of the imaging systems including a beam splitter 318 such asdepicted in FIG. 3C may be preferred in certain situations over theconfiguration depicted in FIG. 3A.

As discussed herein, depressions can be preferred over modulations insome embodiments of the invention. In general, spatially-selectivereflector structures having depressions perform better, particularlywhen the gap between the thin metallic film and the absorbing portion ofthe reflector disk is minimized.

In some embodiments, the linear dimension (i.e., width or diameter) ofthe modulation is at least three wavelengths of interest. Increasing thedimension of the non-uniformity can increase the level of the reflectedsignal. However, if the modulation scheme of the spatially selectiveminor is raster scanning, increasing the dimension of the non-uniformitycan increase the blur in the detected image. Accordingly, in someembodiments, the proper linear dimension for the non-uniformity in thiscase is greater than three wavelengths and less than λF#, where F# isthe F-number of the optics of the system and λ is the radiationwavelength of interest.

FIGS. 13A and 13B depict the power reflection profile of aspatially-selective reflective structure having a depression of lineardimensions 2λ and 3λ, respectively, for a reflective structure whereinthe depression distance and reflector distance from the resistive sheetare

$\frac{\lambda}{2}$ and $\frac{\lambda}{4},$respectively, the sheet resistivity is 377Ω/□, and the radiation isnormally incident to the structure. As depicted by the plots in FIGS.13A and 13B, the reflection profile of the 3λ depression (i.e., FIG.13B) is more effective than the 2λ depression (i.e., FIG. 13A). Themaximum value of the reflection coefficient was 1 for the 3λ depressionand about 0.97 for the 2λ depression. Furthermore, the reflectionprofile for the 3λ depression was more defined than that of the 2λdepression, i.e., the reflection profile have a wider constantreflection profile.

FIGS. 14A and 14B depict the power reflection profile of aspatially-selective reflective structure having a bump distance andreflector distance of

$\frac{\lambda}{2}$ and $\frac{3\lambda}{4},$respectively, a sheet resistivity of 377Ω/□, and radiation normallyincident to the structure.

As depicted in FIGS. 13A-14B, portions of the reflection profilesoscillate around zero. Negative values exists because the reflectioncoefficient is calculated by subtracting the absorption coefficient(i.e., the physical quantity that is calculated from the currents on theresistive sheet) from 1. These oscillations are caused by diffraction ofthe electric field by the edges of the non-uniformities and become moreevident as the distance between the reflector and the resistive sheetincreases or if the modulations are bumps. These diffracted fieldsinterfere with the fields that are incident on the resistive sheet andthe fields that are reflected from the reflector to cause theundulations depicted in FIGS. 13A-14B.

FIG. 15 depicts the power reflection coefficient for a structure that ismodulated by two depressions separated by a gap that varies from 0.1λ to10λ. The depression distance and reflector distance from the resistivesheet were

$\frac{\lambda}{2}$ and $\frac{\lambda}{4},$respectively; the sheet resistivity was 377Ω/□; and the radiation wasnormally incident to the structure.

Each column of the plot is one reflectivity profile corresponding to aseparation as indicated on the x-axis. The plot shows that when thedistance between the depressions (i.e., the separation distance asdepicted on the x-axis of FIG. 15) is greater than 5λ and everysubsequent multiple of a wavelength, the undulations in the regionbetween depressions are minimized. Also, the undulations on the outsidesof the depressions are minimized when the separation is an odd multipleof the wavelength that is greater than or equal to 5λ (e.g., 5λ, 7λ, 9λ,and so on). Furthermore, the undulations almost disappear when thedistance between the depressions is greater than 10λ.

Inter-modulation distances need not be a multiple of the wavelength ofinterest. For example, undulations are acceptably low when theinter-modulation distance is a non-event multiple of a wavelength (e.g.,3.6λ, 4.4λ, 6.7λ, and so on).

FIGS. 16A, 16B, 16C, and 16D depict slices of FIG. 15 and providereflectivity profiles for separations of 4λ, 4.5λ, 5λ, and 10λ,respectively.

Accordingly, in some embodiments of the invention, modulations areseparated by a multiple of a wavelength of interest λ. For examplemodulations can be separated by about 1λ, about 2λ, about 3λ, about 4λ,about 5λ, about 6λ, about 7λ, about 8λ, about 9λ, about 10λ, about 11λ,about 12λ, about 13λ, about 14λ, about 15λ, about 16λ, about 17λ, andthe like.

As will be appreciated by one of ordinary skill in the art, absorptionprofiles can be generated for any potential reflective structure usingexisting software programs. Such modeling can be desirable both tocalculate the matrices discussed herein as well as to optimize theperformance of the reflective structure.

Reflector Disks and Methods of Fabricating the Same

Referring now to FIG. 17 in the context of FIG. 18, a method 1700 offabricating a reflector disk is provided.

In step S1702, a metallic disk 1802 is provided. As discussed herein,the metallic disk 1802 can, in some embodiments, be fabricated from ahighly-conductive metal such as copper, silver, aluminum, and the like.

In step S1704, one or more modulations 1804 (e.g., bumps or depressions)are formed in the metallic disk 1802. Modulations 1804 can be formedwith a variety of techniques including machining, etching, and the like.Alternatively, a metallic disk 1802 can be cast or molded withmodulations 1804. Modulations 1804 can, in some embodiments, bedimensioned according to the principles and equations discussed herein.

In step S1706, a dielectric layer 1806 is applied to the metallic disk1802. The dielectric layer 1806 is preferably transparent to thefrequency of interest. Suitable dielectric materials include, forexample, polyethylene terephthalate (PET) (available under the MYLAR®trademark from E. I. Du Pont de Nemours and Company of Wilmington, Del.)and the like.

In step S1708, the dielectric material 1806 can be machined to produce auniform thickness. In some embodiments, the dielectric material has athickness as discussed herein.

In step S1710, a metallic film 1808 can be deposited on the dielectricmaterial 1806 as discussed herein. The metallic film 1808 can be ametal, for example a highly-conductive metal such as aluminum, copper,silver, gold, and the like. The thickness of the metallic film 1808 can,in some embodiments, be such that the resistivity of the film 1808 isequal to that of free space (i.e., approximately 377Ω/□).

Motors and Viewing Windows

Referring now to FIG. 19A, a spatially-selective reflector device andmotor assembly 1900 a is provided. A motor 1910 spins aspatially-selective reflector structure 1902 a (e.g., aspatially-selective reflector structure as described herein) behind ashield 1904 a defining a viewing window 1906 a. In some embodiments, theshield 1904 a is coated with or fabricated from an absorptive materialsuch as ECCOSORB® materials (available from Emerson & Cuming ofRandolph, Mass.) and radar absorbent materials (RAM).

Structure 1902 a can be rotated continuously and at a constant speed bya spindle motor such as those used in hard disk drives. If the structure1902 a is rotated at a constant speed, the measurement precision islimited only by the integration time of the receiver and the noise levelof the receiver system. For example, the bandwidth of the receiverincreases as the rate of data acquisition increases but an increase inreceiver bandwidth increases the received noise. For an imager of 100 by100 pixels that forms 30 frames per second, 300,000 measurements arerequired (corresponding to a receiver bandwidth of 300 KHz).

If the structure 1902 a is rotated at a constant speed, the receiver canbe triggered to start sampling the input by a sensor that detects thestart of one revolution. This removes the need to have an encoder thatcan measure 1/10,000^(th) of a rotation. If the receiver samples 10,000samples per revolution triggered by the revolution sensor then eachsignal sample corresponds to 1/10,000^(th) of a rotation and eachmeasurement is automatically registered with a rotational position.

In some embodiments, the diameter of the structure 1902 a is betweenabout 2.5 to about 3 times the linear vertical dimension of the imagingwindow 1906 a.

The size of the imaging window 1906 a can be a function of the desiredresolution. For example, to produce an image of 100×100 pixel, whereineach pixel has a 1 mm×1 mm dimension, the imaging window 1906 a will beabout 10 cm×10 cm. The structure 1902 a can have a diameter betweenabout 25 cm and about 30 cm. If the pixel linear size is decreased orincreased by a ratio R while the number of pixels is held constant, thediameter of structure 1902 a will decrease or increase by the same ratioR.

In some situations, the multi-modulation embodiments of the devicesherein may be preferred over a raster scanning embodiments (i.e.,embodiments where a single modulation is within the imaging window 1806at any given time) because (i) the signal received by the receiver ishigher (thereby increasing the signal to noise ratio) and (ii) a smallerstructure can be utilized. However, in situations in which computingpower is limited, a raster scanning embodiment may be preferred.

Without being bound by theory, experimentation has shown that at anygive time, about 20% to about 30% of the imaging window can be “covered”by modulations. This percentage can extend beyond this range so long asthe conditions discussed herein are satisfied.

As depicted in FIG. 19B, a spatially-selective reflector device andmotor assembly 1900 b can be provided for a raster scanning embodiment.Instead of a “large” imaging window 1906 a as in the multiple-modulationassembly 1900 a, shield 1904 b includes an imaging window encompassing asingle modulation. Shield 1904 b can be moved with respect the diameterof structure 1902 b to generate a 2D image from reflections capturedfrom other modulations (not depicted in FIG. 19B). In other embodiments,structure 1902 b has a single modulation and a 1D image is generated.

Calculation of Measurement Matrix

Referring to FIG. 20, the measurement matrix described herein can becalculated according to method 2000.

In step S2002, the imaging window is divided into a desired number ofpixels.

In step S2004, for a first rotational position of the structure, thecenters of modulations visible through the imaging window arecalculated.

In step S2006, the area of intercept between the pixel and a modulationis calculated. In some embodiments, the area of intercept can becalculated using a Monte Carlo algorithm or other similar method. Forexample, if an arbitrary number of points are randomly chosen withineach pixel each point will contribute the local reflection coefficientfor that point (e.g. 1.0, 0.5, and the like) to the integration.

In step S2008, a row of the measure matrix is formed based on the areaof intercept calculated as discussed herein for each pixel in stepS2006.

In step S2010, steps S2004-S2008 are repeated for each subsequentpattern of non-uniformities.

As discussed herein, method 2000 need to only be performed once for agiven disk and a given pixel division in an imaging window. Therefore,it can be computed to the highest accuracy possible using all availabletime and computing resources. As discussed herein, it may be preferablein some embodiments to perform a three-dimensional electromagneticanalysis of the entire structure to determine accurately theabsorption/reflection profile of the disk so that the measurement matrixis calculated accurately.

Once the measurement matrix is computed, its inverse is computed. Again,this operation only needs to be done once.

The system of linear equations can be solved simply by multiplying theinverse of the measurement matrix by the measurement data. Thiscalculation can be performed by hardware and/or software capable ofmultiplying a matrix and a vector. For example, this multiplication canbe performed by one or more field programmable gate arrays (FPGAs)available from Altera Corporation of San Jose, Calif.

Scanning Applications

As discussed herein, embodiments of the invention can be utilized forstandoff scanning (e.g., at large gatherings such as sporting events,parades, rallies, and the like.)

Other embodiments of the invention can be utilized for profiling sensorsthat scan a single line of a moving object and form an image in time.Such an embodiment can be deployed in environment such as airports,office buildings, and the like where individuals are asked to movethrough portal. Advantageously, profiling scanners only require theimaging of a single line at any given moment. (The lines are thencombined to form an image.) Thus, the reflector size and computationpower for image acquisition can be minimized. Both multiple-modulationand raster scanning embodiments described herein can be used inprofiling scanners.

Referring now to FIG. 21, a profiling scanner 2100 incorporating theimaging devices described herein is provided. An individual 2102 entersthe scanner 2100 at a proximal end 2104 and exits at a distal end 2106.The individual can move through the scanner 2100 by walking or can standon an optional moving walkway 2108. As the individual moves through thescanner 2100, one or more imaging devices 2110 a, 2110 b images aplurality of lines (e.g., substantially horizontal lines) of theindividual's body.

In some embodiments one or more optics 2112 a, 2112 b are used to focusthe imager. For example, the optics can 2112 a, 2112 b can focus on thefloor of the distal end 2106 and proximal end 2104, respectively. As theindividual 2102 moves through the scanner, the individuals entire bodywill be imaged without the need to adjust the optics 2112.

EQUIVALENTS

The functions of several elements may, in alternative embodiments, becarried out by fewer elements, or a single element. Similarly, in someembodiments, any functional element may perform fewer, or different,operations than those described with respect to the illustratedembodiment. Also, functional elements (e.g., modules, databases,computers, clients, servers and the like) shown as distinct for purposesof illustration may be incorporated within other functional elements,separated in different hardware, or distributed in a particularimplementation.

While certain embodiments according to the invention have beendescribed, the invention is not limited to just the describedembodiments. Various changes and/or modifications can be made to any ofthe described embodiments without departing from the spirit or scope ofthe invention. Also, various combinations of elements, steps, features,and/or aspects of the described embodiments are possible andcontemplated even if such combinations are not expressly identifiedherein.

INCORPORATION BY REFERENCE

The entire contents of all patents, published patent applications, andother references cited herein are hereby expressly incorporated hereinin their entireties by reference.

The invention claimed is:
 1. A spatially-selective reflective structurecomprising: a partially-conducting slab; and a modulating reflector diskadjacent to the partially-conducting slab, the modulating reflector diskhaving one or more modulations; wherein: the distance between themodulations of the modulating reflector disk and thepartially-conducting slab is defined by the formula${d_{n} = {n\frac{\lambda}{2\sqrt{ɛ_{r}{\cos\left( \phi_{i} \right)}}}}},$ n=1, 2, . . . ; or the distance between a non-modulated surface of themodulating reflector disk and the partially-conducting slab is definedby the formula${d_{r} = \frac{\left( {{2n} - 1} \right)\lambda}{4\sqrt{ɛ_{r}}{\cos\left( \phi_{i} \right)}}},{n = 1},2,{\ldots\mspace{14mu};{and}}$ε_(r) is the relative permittivity of the media between thepartially-conducting slab and the modulations, λ is the wavelength ofinterest, and φ_(i) is the angle of radiation incidence given withrespect to a normal of the spatially-selective reflective structure. 2.The spatially-selective reflective structure of claim 1, wherein the oneor more modulations is a single modulation.
 3. The spatially-selectivereflective structure of claim 1, wherein the one or more modulations isa plurality of modulations.
 4. The spatially-selective reflectivestructure of claim 3, wherein the plurality of modulations are arrangedin a spiral pattern.
 5. The spatially-selective reflective structure ofclaim 3, wherein the plurality of modulations are arranged randomly. 6.The spatially-selective reflective structure of claim 1, wherein theplurality of modulations are arranged such that a matrix having aplurality rows, each with elements corresponding to a fraction of eachpixel in a viewing window projected onto the disk that is backed by amodulation at a distinct rotational position of the disk, has linearlyindependent rows.
 7. The spatially-selective reflective structure ofclaim 1, wherein the plurality of modulations are separated by amultiple of a wavelength of interest.
 8. The spatially-selectivereflective structure of claim 7, wherein the multiple is an oddmultiple.
 9. The spatially-selective reflective structure of claim 7,wherein the multiple is greater than five.
 10. The spatially-selectivereflective structure of claim 1, wherein the one or more modulationshave well-defined edges.
 11. The spatially-selective reflectivestructure of claim 1, wherein the partially-conducting slab is asemiconductor.
 12. The spatially-selective reflective structure of claim1, wherein the partially-conducting slab is a dielectric doped withconductive particles.
 13. The spatially-selective reflective structureof claim 1, wherein the partially-conducting slab comprises: anon-conductive plate; and a thin metal film applied to thenon-conductive plate.
 14. The spatially-selective reflective structureof claim 1, wherein the modulating reflector disk comprises ahighly-conductive metal.
 15. The spatially-selective reflectivestructure of claim 1, wherein the partially-conducting slab and themodulating reflector disk are coupled with one or more mechanicalfasteners.
 16. The spatially-selective reflective structure of claim 1,wherein the modulating reflector disk can rotate independently of thepartially-conducting slab.
 17. The spatially-selective reflectivestructure of claim 1, wherein the partially-conducting slab and themodulating reflector disk are separated by a gap.
 18. Thespatially-selective reflective structure of claim 17, wherein the gap isadjustable.
 19. The spatially-selective reflective structure of claim 1,wherein one or more modulations are depressions.
 20. Thespatially-selective reflective structure of claim 1, wherein the one ormore modulations are bumps.
 21. The spatially-selective reflectivestructure of claim 1, wherein the one or more modulations have across-sectional dimension greater or equal to about one wavelength ofinterest.
 22. The spatially-selective reflective structure of claim 1,wherein the one or more modulations have a cross-sectional dimensiongreater or equal to three wavelengths of interest.
 23. Thespatially-selective reflective structure of claim 1, wherein the one ormore modulations have a cross-sectional dimension less than thewavelength of interest multiplied by an F-number for an optics systemdirecting radiation at the spatially-selective reflective structure.